Activate the yeast: In a small bowl, combine the active dry yeast with a few tablespoons of warm water and a pinch of sugar. Stir and let sit for 5–10 minutes until foamy—this means the yeast is active.
Mix the dry ingredients: In a large mixing bowl, whisk together the flour, sugar, salt, cinnamon, and nutmeg.
Add wet ingredients: Pour the melted butter and the activated yeast mixture into the dry ingredients. Stir until a shaggy dough begins to form.
Knead the dough: Transfer the dough to a floured surface. Knead for 8–10 minutes until it becomes smooth and elastic. Add more flour if it’s too sticky.
First rise: Place the dough in a lightly greased bowl, cover with a clean towel or plastic wrap, and let it rise in a warm spot for 1–2 hours, or until doubled in size.
Shape the doughnuts: Roll the dough out to about ½-inch thickness. Use a doughnut cutter or two round cutters (one large, one small) to cut doughnut shapes. Re-roll scraps to use all the dough.
Second rise: Arrange the doughnuts on a parchment-lined tray, cover lightly, and let rest for 20–30 minutes until slightly puffy.
Heat the oil: In a heavy pot, heat about 2–3 inches of oil to 350°F (175°C). Use a thermometer for accuracy.
Fry the doughnuts: Fry a few at a time, about 1–2 minutes per side or until golden brown. Avoid overcrowding the pot.
Drain and finish: Remove with a slotted spoon and drain on paper towels. While still warm, coat in granulated sugar or dip in your favorite glaze.